The jet stream is getting stronger (and its path becomes more erratic), but the reasoning provided in the article is simplified to the point of being wrong.

The projected warming at the North Pole is much stronger than the projected warming at the equator, decreasing the temperature gradient. However the moisture carrying capacity of air increases exponentially with temperature. Since the equator starts warmer, a given change in temperature has a bigger effect on moisture carrying capacity. It turns out that heating up the equator by one degree Celsius and the North Pole by 2 degrees Celsius increases the moisture capacity gradient, despite the temperature gradient dropping. And that increasing moisture capacity gradient strengthens the jet stream.

(at least that's the intuitive reason they were probably going for. In reality there are many factors and a good bit of "if we simulate it this keeps happening")

Exactly, air currents are becoming stronger with warmer conditions, but the gulfstream being a water current it is expected to become weaker.

The jet stream is also driven by temperature differences. Same with most wind and weather, it's all various forms of heat engine.

(Edit: though apparently the additional moisture in the Tropics more than counteracts any reduction in temperature difference: see link in Retric's comment)

To muddle things even further, there is a (jet) aircraft manufacturer called Gulfstream (https://en.wikipedia.org/wiki/Gulfstream_Aerospace).

...but I fully agree with the rest of your comment.